In this paper we study large-scale optimization problems in multi-view geometry, in particular the Bundle Adjustment problem. In its conventional formulation, the complexity of existing solvers scale poorly with problem size, hence this component of the Structure-from-Motion pipeline can quickly become a bottle-neck. Here we present a novel formulation for solving bundle adjustment in a truly distributed manner using consensus based optimization methods. Our algorithm is presented with a concise derivation based on proximal splitting, along with a theoretical proof of convergence and brief discussions on complexity and implementation. Experiments on a number of real image datasets convincingly demonstrates the potential of the proposed method by outperforming the conventional bundle adjustment formulation by orders of magnitude.

The SCARA-Tau parallel manipulator was derived with the objective to overcome the limited workspace-to-footprint ratio of the DELTA parallel manipulator while maintaining its many benefits. The SCARA-Tau family has later been extended and a large number of variants have been proposed. In this paper, we analyse four of these variants, which together encompass the main differences between all the proposed SCARA-Tau manipulators. The analysed manipulator variants utilise an identical arrangement of five of the six linkages connecting the actuated arms and the manipulated platform and exhibit the same input-output Jacobian. The normalised reciprocal product between the wrench of the sixth linkage and the twist of the platform occurring without this linkage provides a measure on how effectively the sixth linkage constrains the manipulated platform. A comparison of the manipulator variants with respect to this measure demonstrates each variants suitability for specific applications.

Identifying the parameters of a model such that it best fits an observed set of data points is fundamental to the majority of problems in computer vision. This task is particularly demanding when portions of the data has been corrupted by gross outliers, measurements that are not explained by the assumed distributions. In this paper we present a novel method that uses the Least Quantile of Squares (LQS) estimator, a well known but computationally demanding high-breakdown estimator with several appealing theoretical properties. The proposed method is a meta-algorithm, based on the well established principles of proximal splitting, that allows for the use of LQS estimators while still retaining computational efficiency. Implementing the method is straight-forward as the majority of the resulting sub-problems can be solved using existing standard bundle-adjustment packages. Preliminary experiments on synthetic and real image data demonstrate the impressive practical performance of our method as compared to existing robust estimators used in computer vision.

In this paper we study optimization methods for minimizing large-scale pseudoconvex L∞problems in multiview geometry. We present a novel algorithm for solving this class of problem based on proximal splitting methods. We provide a brief derivation of the proposed method along with a general convergence analysis. The resulting meta-algorithm requires very little effort in terms of implementation and instead makes use of existing advanced solvers for non-linear optimization. Preliminary experiments on a number of real image datasets indicate that the proposed method experimentally matches or outperforms current state-of-the-art solvers for this class of problems.

Determining an analytical solution to the inverse kinematics problem for a parallel manipulator is typically a straightforward problem. However, lower mobility parallel manipulators with 2-5 degrees of freedom (DOFs) often suffer from an unwanted parasitic motion in one or more DOFs. For such manipulators, the inverse kinematics problem can be significantly more difficult. This paper contains an analysis of the inverse kinematics problem for a class of 3-DOF parallel manipulators with axis-symmetric arm systems. All manipulators in the studied class exhibit parasitic motion in one DOF. For manipulators in the studied class, the general solution to the inverse kinematics problem is reduced to solving a univariate equation, while analytical solutions are presented for several important special cases.

Although parallel manipulators possess the benefits of high acceleration and accuracy, they typically suffer from a limited workspace to footprint ratio. This paper presents a workspace analysis of two recently proposed axis-symmetric parallel manipulators designed to overcome this problem. The studied manipulators are parametrized, their inverse kinematic models are derived and an in-depth singularity analysis is performed. Next, the architectural parameters are generated for one of the manipulators, using a meta-heuristic algorithm to produce the maximum singularity-free workspace. Thereafter, a second parameter calculation is performed to examine the relationship between maximizing the global conditioning index (GCI) and the resultant achievable workspace for the manipulators.

This paper introduces a novel 5-DOF parallel manipulator with a rotation-symmetric arm system. The manipulator is unorthodox since one degree of freedom of its manipulated platform is unconstrained. Such a manipulator is still useful in a wide range of applications utilizing a rotation-symmetric tool. The manipulator workspace is analyzed for singularities and collisions. The rotation-symmetric arm system leads to a large positional workspace in relation to the footprint of the manipulator. With careful choice of structural parameters, the rotational workspace of the tool is also sizeable.

A family of planar parallel manipulators is investigated and some novel members are proposed. The common feature of the studied manipulators is that the rotation axes of the actuated arms coincide. This feature makes it possible to rotate the whole arm system an infinite number of revolutions around the center of the manipulator. The result is a large workspace in relation to the footprint. Both 2- and 3-DOF variants are presented and the suitability of this family of manipulators for kinematic analysis is demonstrated. Thus, different methods to find optimal manipulability with respect to platform positioning and rotation have been analyzed.

One well acknowledged drawback of traditional parallel kinematic machines (PKMs) is that the ratio of accessible workspace to robot footprint is small for these structures. This is most likely a contributing reason why relatively few PKMs are used in industry today. The SCARA-Tau structure is a parallel robot concept designed with the explicit goal of overcoming this limitation and developing a PKM with a workspace similar to that of a serial type robot of the same size. This paper shows for the first time how a proposed variant of the SCARA-Tau PKM can improve the usability of this robot concept further by significantly reducing the dependence between tool platform position and orientation of the original concept. The inverse kinematics of the proposed variant is derived and a comparison is made between this structure and the original SCARA-Tau concept, both with respect to platform orientation changes and workspace.